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"""Polynomial manipulation algorithms and algebraic objects. """ |
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__all__ = [ |
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'Poly', 'PurePoly', 'poly_from_expr', 'parallel_poly_from_expr', 'degree', |
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'total_degree', 'degree_list', 'LC', 'LM', 'LT', 'pdiv', 'prem', 'pquo', |
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'pexquo', 'div', 'rem', 'quo', 'exquo', 'half_gcdex', 'gcdex', 'invert', |
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'subresultants', 'resultant', 'discriminant', 'cofactors', 'gcd_list', |
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'gcd', 'lcm_list', 'lcm', 'terms_gcd', 'trunc', 'monic', 'content', |
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'primitive', 'compose', 'decompose', 'sturm', 'gff_list', 'gff', |
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'sqf_norm', 'sqf_part', 'sqf_list', 'sqf', 'factor_list', 'factor', |
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'intervals', 'refine_root', 'count_roots', 'all_roots', 'real_roots', |
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'nroots', 'ground_roots', 'nth_power_roots_poly', 'cancel', 'reduced', |
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'groebner', 'is_zero_dimensional', 'GroebnerBasis', 'poly', |
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'symmetrize', 'horner', 'interpolate', 'rational_interpolate', 'viete', |
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'together', |
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'BasePolynomialError', 'ExactQuotientFailed', 'PolynomialDivisionFailed', |
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'OperationNotSupported', 'HeuristicGCDFailed', 'HomomorphismFailed', |
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'IsomorphismFailed', 'ExtraneousFactors', 'EvaluationFailed', |
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'RefinementFailed', 'CoercionFailed', 'NotInvertible', 'NotReversible', |
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'NotAlgebraic', 'DomainError', 'PolynomialError', 'UnificationFailed', |
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'GeneratorsError', 'GeneratorsNeeded', 'ComputationFailed', |
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'UnivariatePolynomialError', 'MultivariatePolynomialError', |
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'PolificationFailed', 'OptionError', 'FlagError', |
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'minpoly', 'minimal_polynomial', 'primitive_element', 'field_isomorphism', |
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'to_number_field', 'isolate', 'round_two', 'prime_decomp', |
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'prime_valuation', 'galois_group', |
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'itermonomials', 'Monomial', |
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'lex', 'grlex', 'grevlex', 'ilex', 'igrlex', 'igrevlex', |
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'CRootOf', 'rootof', 'RootOf', 'ComplexRootOf', 'RootSum', |
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'roots', |
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'Domain', 'FiniteField', 'IntegerRing', 'RationalField', 'RealField', |
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'ComplexField', 'PythonFiniteField', 'GMPYFiniteField', |
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'PythonIntegerRing', 'GMPYIntegerRing', 'PythonRational', |
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'GMPYRationalField', 'AlgebraicField', 'PolynomialRing', 'FractionField', |
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'ExpressionDomain', 'FF_python', 'FF_gmpy', 'ZZ_python', 'ZZ_gmpy', |
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'QQ_python', 'QQ_gmpy', 'GF', 'FF', 'ZZ', 'QQ', 'ZZ_I', 'QQ_I', 'RR', |
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'CC', 'EX', 'EXRAW', |
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'construct_domain', |
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'swinnerton_dyer_poly', 'cyclotomic_poly', 'symmetric_poly', |
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'random_poly', 'interpolating_poly', |
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'jacobi_poly', 'chebyshevt_poly', 'chebyshevu_poly', 'hermite_poly', |
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'hermite_prob_poly', 'legendre_poly', 'laguerre_poly', |
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'bernoulli_poly', 'bernoulli_c_poly', 'genocchi_poly', 'euler_poly', |
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'andre_poly', |
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'apart', 'apart_list', 'assemble_partfrac_list', |
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'Options', |
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'ring', 'xring', 'vring', 'sring', |
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'field', 'xfield', 'vfield', 'sfield' |
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] |
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from .polytools import (Poly, PurePoly, poly_from_expr, |
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parallel_poly_from_expr, degree, total_degree, degree_list, LC, LM, |
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LT, pdiv, prem, pquo, pexquo, div, rem, quo, exquo, half_gcdex, gcdex, |
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invert, subresultants, resultant, discriminant, cofactors, gcd_list, |
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gcd, lcm_list, lcm, terms_gcd, trunc, monic, content, primitive, |
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compose, decompose, sturm, gff_list, gff, sqf_norm, sqf_part, |
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sqf_list, sqf, factor_list, factor, intervals, refine_root, |
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count_roots, all_roots, real_roots, nroots, ground_roots, |
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nth_power_roots_poly, cancel, reduced, groebner, is_zero_dimensional, |
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GroebnerBasis, poly) |
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from .polyfuncs import (symmetrize, horner, interpolate, |
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rational_interpolate, viete) |
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from .rationaltools import together |
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from .polyerrors import (BasePolynomialError, ExactQuotientFailed, |
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PolynomialDivisionFailed, OperationNotSupported, HeuristicGCDFailed, |
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HomomorphismFailed, IsomorphismFailed, ExtraneousFactors, |
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EvaluationFailed, RefinementFailed, CoercionFailed, NotInvertible, |
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NotReversible, NotAlgebraic, DomainError, PolynomialError, |
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UnificationFailed, GeneratorsError, GeneratorsNeeded, |
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ComputationFailed, UnivariatePolynomialError, |
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MultivariatePolynomialError, PolificationFailed, OptionError, |
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FlagError) |
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from .numberfields import (minpoly, minimal_polynomial, primitive_element, |
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field_isomorphism, to_number_field, isolate, round_two, prime_decomp, |
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prime_valuation, galois_group) |
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from .monomials import itermonomials, Monomial |
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from .orderings import lex, grlex, grevlex, ilex, igrlex, igrevlex |
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from .rootoftools import CRootOf, rootof, RootOf, ComplexRootOf, RootSum |
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from .polyroots import roots |
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from .domains import (Domain, FiniteField, IntegerRing, RationalField, |
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RealField, ComplexField, PythonFiniteField, GMPYFiniteField, |
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PythonIntegerRing, GMPYIntegerRing, PythonRational, GMPYRationalField, |
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AlgebraicField, PolynomialRing, FractionField, ExpressionDomain, |
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FF_python, FF_gmpy, ZZ_python, ZZ_gmpy, QQ_python, QQ_gmpy, GF, FF, |
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ZZ, QQ, ZZ_I, QQ_I, RR, CC, EX, EXRAW) |
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from .constructor import construct_domain |
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from .specialpolys import (swinnerton_dyer_poly, cyclotomic_poly, |
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symmetric_poly, random_poly, interpolating_poly) |
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from .orthopolys import (jacobi_poly, chebyshevt_poly, chebyshevu_poly, |
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hermite_poly, hermite_prob_poly, legendre_poly, laguerre_poly) |
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from .appellseqs import (bernoulli_poly, bernoulli_c_poly, genocchi_poly, |
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euler_poly, andre_poly) |
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from .partfrac import apart, apart_list, assemble_partfrac_list |
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from .polyoptions import Options |
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from .rings import ring, xring, vring, sring |
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from .fields import field, xfield, vfield, sfield |
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